A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines

Annalisa Buffa; Yvon Maday; Francesca Rapetti

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 2, page 191-228
  • ISSN: 0764-583X

Abstract

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The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the second one based on iso-parametric finite elements in both the static and moving parts. The coupling is obtained by means of the mortar element method (see [7]) and the approximation on the whole domain turns out to be non-conforming. In both cases optimal error estimates are provided. Numerical tests are then proposed in the case of standard first order finite elements to test the reliability and precision of the method. An application of the method to study the influence of the free part movement on the currents distribution is also provided.

How to cite

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Buffa, Annalisa, Maday, Yvon, and Rapetti, Francesca. "A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.2 (2001): 191-228. <http://eudml.org/doc/194047>.

@article{Buffa2001,
abstract = {The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the second one based on iso-parametric finite elements in both the static and moving parts. The coupling is obtained by means of the mortar element method (see [7]) and the approximation on the whole domain turns out to be non-conforming. In both cases optimal error estimates are provided. Numerical tests are then proposed in the case of standard first order finite elements to test the reliability and precision of the method. An application of the method to study the influence of the free part movement on the currents distribution is also provided.},
author = {Buffa, Annalisa, Maday, Yvon, Rapetti, Francesca},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Eddy currents problem; non-conforming finite element approximation; domain decomposition methods; eddy currents problem; nonconforming finite element approximation; approximation of Maxwell equations; curved finite elements; mortar element method; error estimates},
language = {eng},
number = {2},
pages = {191-228},
publisher = {EDP-Sciences},
title = {A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines},
url = {http://eudml.org/doc/194047},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Buffa, Annalisa
AU - Maday, Yvon
AU - Rapetti, Francesca
TI - A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 2
SP - 191
EP - 228
AB - The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the second one based on iso-parametric finite elements in both the static and moving parts. The coupling is obtained by means of the mortar element method (see [7]) and the approximation on the whole domain turns out to be non-conforming. In both cases optimal error estimates are provided. Numerical tests are then proposed in the case of standard first order finite elements to test the reliability and precision of the method. An application of the method to study the influence of the free part movement on the currents distribution is also provided.
LA - eng
KW - Eddy currents problem; non-conforming finite element approximation; domain decomposition methods; eddy currents problem; nonconforming finite element approximation; approximation of Maxwell equations; curved finite elements; mortar element method; error estimates
UR - http://eudml.org/doc/194047
ER -

References

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